Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Artefact-oriented business process modelling: an ontological dependency approach

Business process modelling can help an organisation better understand and improve its business processes. Most business process modelling methods adopt a task- or activity-based approach to identifying business processes. Within our work, we use activity theory to categorise elements within organisations as being either human beings, activities or artefacts. Due to the direct relationship between these three elements, an artefact-oriented approach to organisation analysis emerges. Organisational semiotics highlights the ontological dependency between affordances within an organisation. We analyse the ontological dependency between organisational elements, and therefore produce the ontology chart for artefact-oriented business process modelling in order to clarify the relationship between the elements of an organisation. Furthermore, we adopt the techniques from semantic analysis and norm analysis, of organisational semiotics, to develop the artefact-oriented method for business process modelling. The proposed method provides a novel perspective for identifying and analysing business processes, as well as agents and artefacts, as the artefact-oriented perspective demonstrates the fundamental flow of an organisation. The modelling results enable an organisation to understand and model its processes from an artefact perspective, viewing an organisation as a network of artefacts. The information and practice captured and stored in artefact can also be shared and reused between organisations that produce similar artefacts.

An ontological approach to personalized medical knowledge recommendation

Knowledge recommendation has become a promising method in supporting the clinicians decisions and improving the quality of medical services in the constantly changing clinical environment. However, current medical knowledge management systems cannot understand users requirements accurately and realize personalized recommendation. Therefore this paper proposes an ontological approach based on semiotic principles to personalized medical knowledge recommendations. In particular, healthcare domain knowledge is conceptualized and an ontology-based user profile is built. Furthermore, the personalized recommendation mechanism is illustrated.

An ontological approach to personalized medical knowledge matching

Knowledge management has become a promising method in supporting the clinicians′ decisions and improving the quality of medical services in the constantly changing clinical environment. However, current medical knowledge management systems cannot understand users′ requirements accurately and realize personalized matching. Therefore this paper proposes an ontological approach based on semiotic principles to personalized medical knowledge matching. In particular, healthcare domain knowledge is conceptualized and an ontology-based user profile is built. Furthmore, the personalized matching mechanism and algorithm are illustrated.

Developing a knowledge management system using an ontological approach in global organisation

This paper introduces an ontology-based knowledge model for knowledge management. This model can facilitate knowledge discovery that provides users with insight for decision making. The users requiring the insight normally play different roles with different requirements in an organisation. To meet the requirements, insights are created by purposely aggregated transnational data. This involves a semantic data integration process. In this paper, we present a knowledge management system which is capable of representing knowledge requirements in a domain context and enabling the semantic data integration through ontology modeling. The knowledge domain context of United Bible Societies is used to illustrate the features of the knowledge management capabilities.

Transreal proof of the existence of universal possible worlds

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any transreal numbers with the result being a transreal number [1]. In particular division by zero is allowed. It is proved, in [3], that transreal arithmetic is consistent and contains real arithmetic. The entire set of transreal numbers is a total semantics that models all of the semantic values, that is truth values, commonly used in logics, such as the classical, dialetheaic, fuzzy and gap values [2]. By virtue of the totality of transreal arithmetic, these logics can be implemented using total, arithmetical functions, specifically operators, whose domain and counterdomain is the entire set of transreal numbers

A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Improving the health forecasting alert system for cold weather and heat-waves in England: a proof-of-concept using temperature-mortality relationships

Objectives In this study a prototype of a new health forecasting alert system is developed, which is aligned to the approach used in the Met Office’s (MO) National Severe Weather Warning Service (NSWWS). This is in order to improve information available to responders in the health and social care system by linking temperatures more directly to risks of mortality, and developing a system more coherent with other weather alerts. The prototype is compared to the current system in the Cold Weather and Heatwave plans via a case-study approach to verify its potential advantages and shortcomings. Method The prototype health forecasting alert system introduces an “impact vs likelihood matrix” for the health impacts of hot and cold temperatures which is similar to those used operationally for other weather hazards as part of the NSWWS. The impact axis of this matrix is based on existing epidemiological evidence, which shows an increasing relative risk of death at extremes of outdoor temperature beyond a threshold which can be identified epidemiologically. The likelihood axis is based on a probability measure associated with the temperature forecast. The new method is tested for two case studies (one during summer 2013, one during winter 2013), and compared to the performance of the current alert system. Conclusions The prototype shows some clear improvements over the current alert system. It allows for a much greater degree of flexibility, provides more detailed regional information about the health risks associated with periods of extreme temperatures, and is more coherent with other weather alerts which may make it easier for front line responders to use. It will require validation and engagement with stakeholders before it can be considered for use.